Does Regulatory Jurisdiction Affect the Quality of Investment-Adviser Regulation?

The Dodd-Frank Act shifted regulatory jurisdiction over “ midsize” investment advisers from the SEC to state-securities regulators. Client complaints against midsize advisers increased relative to those continuing under SEC oversight by 30 to 40 percent of the unconditional probability. Complaints increasingly cited fiduciary violations and rose more where state regulators had fewer resources. Advisers responding more to weaker oversight had past complaints, were located farther from regulators, faced less competition, had more conflicts of interest, and served primarily less-sophisticated clients. Our results inform optimal regulatory design in markets with informational asymmetries and search frictions. (JEL G24, G28, K22, L51, L84)

Conditional Probability

Conditional probability has been put to many uses in philosophy, and several proposals have been made regarding its relation to unconditional probability, especially in cases involving infinitely many alternatives that may have probability 0. This chapter briefly summarizes some of the literature connecting conditional probabilities to probabilities of conditionals and to Humphreys' Paradox for chances, and then investigates in greater depth the issues around probability 0. Approaches due to Popper, Rényi, and Kolmogorov are considered. Some of the limitations and alternative formulations of each are discussed, in particular the issues arising around the property of “conglomerability” and the idea that conditional probabilities may depend on a conditioning algebra rather than just an event.

A Proposed Bayesian Updating Approach to Update the Failure Probability of a Corrosion Defect After Performing Fitness for Service Based on API 579-1/ASME FFS-1

Using Risk-Based Inspection (RBI) and Fitness for Service (FFS) approaches to manage the integrity of pressure equipment has been the industries best practice for almost a decade. However, there had never been a procedural link between these two approaches in a way that when one performed FFS analysis on a defect, one could update the risk accordingly. This paper proposes a quantitative method to refresh the risk calculated in the RBI process when FFS analysis is completed on a locally thinned area. The proposed approach applies a probabilistic technique by considering the Remaining Strength Factor (RSF) from API 579-1/ASME FFS-1 as the limit state equation and assuming the corrosion rate as a distribution variable to estimate the unconditional probability of failure. This value is then modified using a Bayesian updating method allowing for the conditional probability to represent a new failure likelihood which could be utilized in the RBI planning.

Topological Information Content and Expressiveness of Function Models in Mechanical Design

In this paper, two approaches for computing the topological information content of function models in mechanical engineering design are developed and compared. Previously, a metric for computing information content of functions and flows within function models was proposed. Here, this metric is evolved to include the information contained in the connections between flows and functions in a function model. The first approach is based on uniform unconditional probability of a flow connecting any two functions within the model. The second approach is based on additional knowledge that the functions and flows in a model have limited compatibility, thereby, reducing the choices for origin and destination functions for each flow. This additional knowledge is represented using a new graphical representation supported by syntactic grammar rules. Both approaches are then applied to an example function model. Comparison between the approaches shows that the inclusion of this additional knowledge increases the expressiveness by reducing the uncertainty associated with function models.

Topological Information Content and Expressiveness of Function Models in Mechanical Design

In this paper, two approaches for computing the topological information content of function models in mechanical engineering design are developed and compared. Previously a metric for computing information content of functions and flows within function models was proposed. Here this metric is adapted to compute the information contained in the resulting connections of flows between functions in a function model. The first approach is based on uniform unconditional probability of a flow connecting any two functions within the model. The second approach is based on additional knowledge that the functions and flows in a model have limited compatibility, thereby reducing the choices for origin and destination functions for each flow. This additional knowledge is represented using a new graphical representation supported by syntactical grammar rules. Both approaches are then applied to an example function model. Comparison between the approaches shows that the inclusion of compatibility knowledge increases the expressiveness of function representations and reduces the uncertainty of function models.

A Likelihood-Ratio Test of Twin Zygosity Using Molecular Genetic Markers

The importance of using multiple polymorphic genetic markers to determine unambiguously whether a twin pair is monozygotic (MZ) or dizygotic (DZ) has long been recognized. Concordance among a set of markers is used as evidence of monozygosity, as it would be improbable for DZ twins to be concordant at a large number of polymorphic loci. Several sources give a formula for the probability of two DZ twins sharing the same genotype at a locus, assuming knowledge of allele frequencies but not of either twin's genotype; this probability can be used to determine whether a set of markers will reliably distinguish between MZ and DZ status in a randomly selected twin pair. If the shared genotype is known, however, the likelihood-ratio test (LRT) of the null hypothesis of dizygosity against the alternative hypothesis of monozygosity takes into account the observed genotype and, by the Neyman-Pearson lemma, is the most powerful test of its size. The LRT is equivalent to conditioning on the genotype of one of the twins, and computing the probability, assuming DZ status, of the other twin sharing that genotype. The resultingpvalues are frequently lower than those produced by the unconditional probability, especially if rare alleles are observed. The unconditional probability can be recapitulated from conditional probabilities by averaging across all of the conditioned sibling's possible genotypes. To illustrate properties of the LRT applied to multiple markers, the probability distribution of the LRTpvalue is computed from allele frequencies of twelve unlinked markers published in Elbaz et al. (2006) and compared with thepvalue computed from unconditional probabilities.

A logic with higher order conditional probabilities

We investigate probability logic with the conditional probability operators This logic, denoted LCP, allows making statements such as: P?s?, CP?s(? | ?) CP?0(? | ?) with the intended meaning "the probability of ? is at least s" "the conditional probability of ? given ? is at least s", "the conditional probability of ? given ? at most 0". A possible-world approach is proposed to give semantics to such formulas. Every world of a given set of worlds is equipped with a probability space and conditional probability is derived in the usual way: P(? | ?) = P(?^?)/P(?), P(?) > 0, by the (unconditional) probability measure that is defined on an algebra of subsets of possible worlds. Infinitary axiomatic system for our logic which is sound and complete with respect to the mentioned class of models is given. Decidability of the presented logic is proved.

A BAYESIAN METANETWORK

Bayesian network (BN) is known to be one of the most solid probabilistic modeling tools. The theory of BN provides already several useful modifications of a classical network. Among those there are context-enabled networks such as multilevel networks or recursive multinets, which can provide separate BN modelling for different combinations of contextual features' values. The main challenge of this paper is the multilevel probabilistic meta-model (Bayesian Metanetwork), which is an extension of traditional BN and modification of recursive multinets. It assumes that interoperability between component networks can be modeled by another BN. Bayesian Metanetwork is a set of BN, which are put on each other in such a way that conditional or unconditional probability distributions associated with nodes of every previous probabilistic network depend on probability distributions associated with nodes of the next network. We assume parameters (probability distributions) of a BN as random variables and allow conditional dependencies between these probabilities. Several cases of two-level Bayesian Metanetworks were presented, which consist on interrelated predictive and contextual BN models.

Bayesian Approaches to Plant Disease Forecasting

Prediction of disease occurrence is a well known historical theme, and has begun to receive new interest due to internet-based prediction systems. The evaluation of these systems in a quantitative manner is an important step if they are to be used in modern agricultural production. Bayes's theorem is one way in which the performance of such predictors can be studied. In this way, the conditional probability of pest occurrence after a positive or negative prediction can be compared with the unconditional probability of pest occurrence. Both the specificity and the sensitivity of the predictive system are needed, along with the unconditional probability of pest occurrence, in order to make a Bayesian analysis. If there is little information on the prior probability of disease, most predictors will be useful, but for extremely common or extremely rare diseases, a Bayesian analysis indicates that a system predicting disease occurrence or non-occurrence will have limited usefulness. Accepted for publication 29 January 2002. Published 13 November 2003.